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Discoveries

Bounds that moved, objects that beat a record and algorithms with fewer operations. Each record target is a quantity with a direction and the history of who held each value; Frontiers draws each history as a staircase.

77 targets 27 records held by a machine 14 matched the best known 3 objects rebuilt here

Every target

Algorithms

AlphaEvolve problems

Analytic number theory

Discrete geometry

Extremal combinatorics

Number theory

How records are read

Why a register needs targets

Much of what AI has contributed to mathematics is a better bound or a new object rather than a settled proposition, so the register holds record targets beside its statements, each with the history of its values and who reached them.

A machine holds the record on 27 of these and matched without beating it on 14 more; the two standings are counted separately. Where a source records only where a construction stands, not its value, the value is left empty.

Record standings
below
Did not reach the best known value
matched
Equalled the best known value
record
Best known value
superseded
Held the record, since beaten
unstated
No standing recorded at source

Evidence uses the same ladder as a proof. For an object, V3 means the thing was rebuilt and tested against the constraints of its own problem.